Semiclassical theory of a quantum pump

In a quantum charge pump, the periodic variation of two parameters that affect the phase of the electronic wave function causes the flow of a direct current. The operating mechanism of a quantum pump is based on quantum interference, the phases of interfering amplitudes being modulated by the external parameters. In a ballistic quantum dot, there is a minimum time before which quantum interference cannot occur: the Ehrenfest time tau(E). Here we calculate the current pumped through a ballistic quantum dot if tau(E) is comparable to the mean dwell time tau(D). Remarkably, we find that the pumped current has a component that is not suppressed if tau(E)>tau(D).